What's 'cheap', this is all relative?
Most people won't find anywhere cheap in central London, especially in the middle of the tourist season.
Check TripAdvisor, you'll see reviews form a lot of actual users.
www.laterooms.com. I have used this site a lot, and the experience was pretty good, up until the height of the tourist season, when rooms got booked up so fast that it was difficult to find anywhere at all.
What's your budget?